We will have our annual winter school this January 6-10. Our speaker is Huy
Pham from IAS.
Please find below the course description and more details here at our
course homepage:
https://www.ibs.re.kr/ecopro/winter-2025/
It will be held offline at IBS and also streamed over zoom. Join us :)
- Time: everyday Jan 6 to Jan 10, 2025, offline at IBS headquarter B332.
Online: *9:00-10:30am (Beijing)*, *10:00-11:30am (Seoul)*.
- *Zoom: 981 0186 8315, PW: 250106*
Cheers,
Hong
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*Recent developments in probabilistic combinatorics: New synergies*
Recent developments in probabilistic combinatorics have brought about
synergistic interactions across multiple disciplines, including extremal
combinatorics, probability theory and theoretical computer science. This
mini-course aims to give an introduction to some of these developments and
interactions.
In the first part of the mini-course, we will discuss the Kahn-Kalai
conjecture on thresholds and expectation thresholds and its close relation
to Talagrand's selector process conjecture in probability theory. We will
also touch on several subsequent developments of the proof technique in
extremal combinatorics, probability theory and theoretical computer
science.
The Kahn-Kalai conjecture opens up a new avenue on thresholds of
interesting properties in random graph models. Yet, while it relates
thresholds to the expectation thresholds, estimation of the latter remains
a highly challenging task in general. Recent developments have found close
connections between this task and previous fundamental developments in
extremal combinatorics, such as the regularity method. In the second part
of the mini-course, I will briefly overview classical aspects of the
regularity method before discussing its new applications to thresholds and
other problems in probabilistic combinatorics.
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